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It could dump up to 6 inches of rain over much of Florida and southeast Georgia

The storm is expected to travel up the East Coast on Friday and Saturday

(CNN) -- Tropical Storm Andrea is set to wallop Florida with torrential rain as it prepares to make landfall Thursday.

The first named storm of the Atlantic hurricane season made its debut Wednesday by pummeling Cuba with heavy downpours.

As of 8 a.m. ET Thursday, Andrea was 160 miles west of Tampa, Florida, and was headed north-northeast at 14 mph, the National Hurricane Center said.

Though it's set to soak Tallahassee, Sue Carpenter doesn't expect it to deter many of her dedicated Pilates students, she told CNN less than an hour before Lifelong Fitness Pilates studio opened. If it gets bad, she may close, she said. But by 8 a.m., none of her private class clients had called to cancel.

"They're dedicated," she said.

Across town at Mike's Liquor and Beer Barn, the delivery trucks arrived earlier than usual Wednesday morning. "We'll see an upswing" in business during the morning, he said.

"But I think it's not gonna be anything special, nothing real bad. It's been so long since Tallahassee had a storm. Today I think people are just now realizing it's coming."

The center of Andrea is expected to reach the Florida Panhandle late Thursday before cutting across southern Georgia and moving up the East Coast on Friday and Saturday.

Andrea is expected to unleash 3 to 6 inches of rain over much of Florida and southeastern Georgia and as much as 8 inches in some areas. The eastern parts of North and South Carolina could see up to 4 inches of rain, the National Hurricane Center said.

"The combination of a storm surge and the tide will cause normally dry areas near the coast to be flooded by rising waters," the hurricane center said.

The Florida peninsula could also see a few tornadoes Thursday, forecasters said.

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